An Isaac Newton Institute Workshop

Non-Equilibrium Dynamics of Interacting Particle Systems

Field-Theoretic Approaches to Interacting Particle Systems

Abstract

It is explained how field-theoretic methods and the dynamic
renormalization group (RG) can be applied to study the universal
scaling properties of interacting particle systems far from thermal
equilibrium that either undergo a continuous phase transition or
display generic scale invariance It is described how the master
equation for stochastic particle reaction processes can be mapped onto
a field theory action. The RG is then employed to analyze the ensuing
power laws in simple diffusion-limited annihilation reactions as well
as generic continuous transitions from active to inactive, absorbing
states, which are characterized by the power laws of (critical)
directed percolation. Certain other important universality classes
including dynamic percolation and parity-conserving branching and
annihilating random walks are discussed, and some open issues are
mentioned.